The artificial viscosity method was originally introduced by Von Neuman and Richtmeyer [R. D. Rchtmeyer and K. W. Morton, inDifferenceMethodsforInitialValueProblem(Interscience, New York, 1967)] to spread the shock over several cells of the mesh. This method is useful if the physical phenomena present in the shock front are not of interest. In some cases, such as polymer, the amount of viscosity is large enough to spread the front shock naturally. In our problem, pseudoviscosity is ignored. A stability analysis shows that the time step restrictions for stability can be less stringent than with pseudoviscosity.